On 11 March 1958, in Mars Bluff, South Carolina, a man called Walter Gregg was building shelves in his shed with his son, when a Mark 6 atom bomb landed in his yard. Mrs Gregg was inside, sewing. The little Gregg girls were playing outside. The fissile core of the bomb had been removed for safer transit, but the explosives that powered it nonetheless blew the Gregg house to bits, killing half a dozen of the Gregg chickens. In military talk this sort of thing is known as a "broken arrow", an accident involving nuclear weapons that falls short of causing risk of war, and Schlosser's book is about the several dozens of these that have happened – counting only those of US origin – since the atomic bomb was invented in 1945. The next-up sort of accident is called a Nucflash. So far, it hasn't happened, but Schlosser considers this due as much to luck as anything else.

Around the time of the Mars Bluff "mishap", Peter George, a former RAF officer, published Red Alert, the novel that became the basis of Stanley Kubrick's great nuclear-deterrence satire, Dr Strangelove (1964). Both novel and movie concern the blackly entertaining efforts of politicians and military to get back the weapons launched on the Soviet Union by a mad American general, and highlighted two big real-life strategic problems. By the time Dr Strangelove came out, atomic weapons were designed for delivery not by plane but rocket, a matter of minutes after launching. There wouldn't be time for second thoughts or frantic horse-trading of the sort the fictional scenarios showed. Also, no "nuclear hotline" between the White House and the Kremlin even existed until 1963, after the Cuban missile crisis, during which top-level messages between Washington and Moscow had been delivered by bike.

Eric Schlosser is most famous for Fast Food Nation (2000). Like that book, his new one aims to "pierce a false sense of comfort", in this case the popular assumption that because all the talk at the moment is about Syria, drone strikes and chemical stockpiles, the threat of nuclear escalation has gone away for good. It hasn't, is Schlosser's miserable message. "They are out there, soulless and mechanical, sustained by our denial – and they work." In Fast Food Nation, Schlosser reported on the ways the food industry compromised hygiene and safety in pursuit of its profits. In this book, he's interested in how "the effort to control nuclear weapons – to ensure that one doesn't go off by accident" is undermined, over and over again, by demands from the military for bombs they can trust to explode. The conflict is partly one of "mindset" – military operatives are used to danger, and are comfortable taking risks that most people cannot live with. But mainly it's to do with how uniquely lethal nuclear weapons are, and the necessarily labyrinthine safety procedures that come with them – "the mixture of human fallibility and technological complexity that can lead to disaster", and sometimes does.

The story alternates between two main strands. One is a 70-year history of nuclear weapons in America, from the Manhattan project in the 1940s to the ending of the cold war. The other is a blow-by-blow account of one particular "mishap", at the Titan II silo near Damascus, Arkansas, in September 1980, when a dropped tool pierced a missile shell and caused a fuel leak – "Oh, man," as one of the maintenance men thought when he saw the stuff spraying out. "Oh, man. This is not good." That tiny slip might well have caused a nuclear detonation, and it was hours before people could be sure that it hadn't. As it turned out, the fuel leak resulted nevertheless in poisoned lungs and broken bones, ignominy, lawsuits, much bitterness and the death of one man, senior airman David L Livingston, described by Schlosser as "a 22-year-old missile repairman from Ohio with a fondness for motorcycles" and who is remembered by the colleagues who tried to rescue him as begging them not to tell his mother that he'd been hurt.

The Titan II, Schlosser tells us, was the largest intercontinental ballistic missile ever built by the US, 10ft in diameter and 103ft tall, with a nine-megaton thermo-nuclear warhead inside its black-painted nose-cone, "primed, cocked, ready to go". There were 18 of them dotted around rural Arkansas, "buried off back-country roads, near small farms and little towns". This particular one was sited at Launch Complex 374-7 in the foothills of the Ozark mountains, near the small town of Damascus. According to whistleblowing insiders cited by Schlosser, the missiles were known to be old and leaky, "a disaster waiting to happen". Personnel were known to be undertrained, overworked, and extremely young. The subject of what went wrong at Launch Complex 374-7 is returned to repeatedly, each time seen from a different perspective, each time with a further layer of mistakes and malfunctions picked up. It's a horrifying tale of bad design and carelessness and short-cutting, with a lot of dithering from the officers in the control centre and courage from the men on the ground. Clearly, it's a story that needs to be widely known.

I'm not convinced, however, that Schlosser has found the best way to tell it. The terrain, of course, is difficult – horrible weapons, dozens of characters, serial numbers, placenames, and all fogged by doubt and confusion and unattributability, as well as by the "cloud of white vapour … like steam from a boiling kettle" pouring out of the bomb. Schlosser, it's obvious, has done a stupendous amount of research, talking to everybody, chasing up every note and file that can be read, and with 92 pages of notes at the end of the book to prove it – fascinating, a masterclass in itself as to how this sort of investigative work is done. And yet in some ways, this very exhaustiveness can become exhausting. The historical parts of the book, for example, are loaded with detail, but without many quotes to anchor them. This happens, I'd guess, because big-player sources have asked not to be quoted, but makes it difficult to follow the course of events.

The Damascus story is also laborious-going. The timeline keeps jumping forwards and backwards, from the accident in Complex 374-7 to another one that happened in 373-4, then back again to the first one, only now seen from somebody else's point of view. Schlosser's conclusions, on the other hand, are clear. Although the cold war is now more than 20 years over, the US still has an arsenal of 4,650 nuclear weapons, aimed at Russia, China, North Korea, Syria and Iran, with potential to swivel round at other enemies as they happen to pop up. Russia has about 1,500 "strategic" – ie long-range, intercontinental – missiles and maybe 2,000 "tactical" ones, which are the shorter-range weapons for use in what used to be called "the European theatre", in other words, us. We've got some, France has some, India and Pakistan aim theirs at each other, Israel keeps its collection secret and China hides its in "an underground Great Wall". Because they are so dreadfully dangerous, nuclear weapons generate particular politics around them – authoritarian, secretive, undemocratic. Even so, mistakes happen, and it's even possible that authoritarianism and secrecy make the problems worse. Nuclear weapons are not like Wikipedia, on which anybody can spot a mistake and write in.

And yes, it's true so far that "none of the roughly 70,000 nuclear weapons built by the US since 1945 has ever detonated inadvertently or without proper authorisation." But the US is an extremely rich, technologically sophisticated country, and as the inventor of nuclear weapons in the first place, the one furthest advanced in developing "the organisational skills and safety culture necessary to manage them". And even it, as Schlosser has shown, has only narrowly avoided nuclear disaster. "Other countries, with less hard-earned experience, may not be as fortunate."

One measure of a nation's technological proficiency, as Schlosser says, is its rate of industrial accidents – a topic explored to great effect in Fast Food Nation. "That rate is about two times higher in India, three times higher in Iran, and four times higher in Pakistan than it is in the United States." Across the world in the early 21st century, nuclear weapons have become "a symbol of power and source of national pride". But the threats they pose are as grave to the countries that possess them as they are to everybody else.